Abstract
In this paper, a nonlinear mathematical model with diffusion is taken into account to review the dynamics of Lengyel–Epstein chemical reaction model to describe the oscillating chemical reactions. For this purpose, the dimensionless Lengyel–Epstein model with diffusion and homogeneous boundary condition is considered. The steady states with and without diffusion of the Lengyel–Epstein model are studied. The basic reproductive number is computed and the global steady states for the system are calculated. Numerical results are offered for two systems using three well known techniques to validate the main outcomes. The consequences established from this qualitative study are supported by numerical simulations characterized by distinct programs, adopting forward Euler method, Crank–Nicolson method, and nonstandard finite difference method.
Highlights
The chemical reactions as the Belousov–Zhabotinsky reaction and the Briggs–Rauscher reaction are exceptional
Comment 2 Merging the activator–inhibitor condition (18) with the steady state condition given in Proposition 2, we discover that the condition mψ2(μ) > – ψ(μ) + 4μψ (μ) > 0 makes the system (6) a diffusion free stable activator–inhibitor structure
7 Conclusion In this article, we consider a nonlinear model with diffusion to review the dynamics of Lengyel–Epstein reaction model describing oscillating chemical reactions
Summary
The chemical reactions as the Belousov–Zhabotinsky reaction and the Briggs–Rauscher reaction are exceptional. It is experimentally seen that the concentrations of chlorite and iodide ions fluctuate over numerous orders of level through an oscillation, whereas the concentrations of chlorine dioxide and malonic acid vary slowly. These concentrations may be considered as constants, and actions of the system may be estimated by a two-variable specimen including only the concentrations of iodide and chlorine ions. Comment 2 Merging the activator–inhibitor condition (18) with the steady state condition given in Proposition 2, we discover that the condition mψ2(μ) > – ψ(μ) + 4μψ (μ) > 0 makes the system (6) a diffusion free stable activator–inhibitor structure.
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